Henry will have run a total of 1540 miles on his new running shoes after 5 weeks.
Explanation:To find the total mileage on Henry's shoes after 5 weeks, we need to calculate the distance he runs each week and add them up.
In week 1, Henry runs 20 miles per day, so the total distance he runs in week 1 is 20 miles * 7 days = 140 miles.
In week 2, he adds 12 miles to his daily routine, so he runs 20 miles + 12 miles = 32 miles per day. The total distance he runs in week 2 is 32 miles * 7 days = 224 miles.
We can continue this pattern for the remaining weeks:
Week 3: 44 miles per day, total distance = 44 miles * 7 days = 308 miles
Week 4: 56 miles per day, total distance = 56 miles * 7 days = 392 miles
Week 5: 68 miles per day, total distance = 68 miles * 7 days = 476 miles
The total mileage on Henry's shoes after 5 weeks is the sum of the total distances in each week: 140 + 224 + 308 + 392 + 476 = 1540 miles.
A motorcyclist heading east through a small Iowa town accelerates after he passes a signpost at x=0 marking the city limits. His acceleration is constant (4.0 m/s2). At time t =0 he is 5 m east of the signpost and has a velocity of 15 m/s. (a) find his position and velocity at time t=2 sec. (b) where is the motor cyclist when his velocity is 25 m/s?
Answer:
a) 43 m b) 55 m
Step-by-step explanation:
a) From question at t = 0, initial velocity [tex]V_{o}[/tex] = 15 m/s
Using equation of motion, [tex]S = V_{o}t + \frac{1}{2} at^{2}[/tex] ; at t = 2 secs , a = 4 m/[tex]s^{2}[/tex]
S = (15 x 2) + (0.5 X 4 x [tex]2^{2}[/tex])
S = 30 + 8 = 38 m , Therefroe;
car is (38 + 5)m from the sign post
car is 43 m from the sign post at t = 2 secs
b) Also from equation of motion, [tex]V^{2} = V_{o} ^{2} + 2aS[/tex]
[tex]25^{2} = 15^{2}[/tex] + (2 x 4 x S)
625 - 225 = 8S
S = 50 m
Car is (50 + 5) m from the sign post
Car is 55 m from the sign post at V = 25 m/s
At t=2s, the motorcyclist is at position 29m east of the signpost with a velocity of 23m/s. When his velocity is 25m/s, he is at a position 38.75m east of the signpost.
Explanation:Given that the motorcyclist starts 5 m east of the signpost with an initial velocity of 15 m/s and a constant acceleration of 4.0 m/s2, we can use the equation of motion to find his position and velocity at any given time.
(a) At t=2s, the motorcyclist's position (x) and velocity (v) can be determined using the following two equations respectively:
Position (x) = x0 + v0*t + 0.5*a*t2 = 5 m + 15 m/s*2s + 0.5*4.0 m/s2* (2s)2 = 29 mVelocity (v) = v0 + a*t = 15 m/s + 4.0 m/s2*2s = 23 m/s
(b) When the velocity is 25 m/s, the time can be calculated using the equation v = v0 + a*t. By setting v=25m/s, v0=15m/s, and a=4.0m/s2, we get t = (25m/s-15m/s) / 4.0m/s2 = 2.5s. Substituting this time into the position equation gives x = 5m + 15m/s*2.5s + 0.5*4.0m/s2*(2.5s)2, which results in the motorcyclist being at position 38.75 m.
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PLEASE HELPPP!!! QUESTION AND ANSWERS IN PICTURE !
answer is C: [tex]\frac{EF}{DF}[/tex]
Answer:option C is the correct answer
Step-by-step explanation:
Triangle DEF is a right angle triangle.
From the given right angle triangle,
DF represents the hypotenuse of the right angle triangle.
With m∠θ as the reference angle,
EF represents the adjacent side of the right angle triangle.
DE represents the opposite side of the right angle triangle.
To determine Cos ∠θ, we would apply
the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos θ = EF/DF
PLZ HELP THIS IS TIMED!!!!
Which formula can be used to describe the sequence? Negative two-thirds, −4, −24, −144,... f(x) = 6(negative two-thirds) Superscript x minus 1 f(x) = −6(Two-thirds) Superscript x minus 1 f(x) = Negative two-thirds(6)x − 1 f(x) = Two-thirds(−6)x − 1
Answer:
For the sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...
Hence the formula [tex]f(x)=-\frac{2}{3}(6)^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence
Step-by-step explanation:
Given sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...
To find the formula to describe the given sequence :
Let [tex]a_1=\frac{-2}{3}[/tex] ,[tex]a_2=-4[/tex] ,[tex]a_3=-24[/tex],...
First find the common ratio
[tex]r=\frac{a_2}{a_1}[/tex] here [tex]a_1=\frac{-2}{3}[/tex] and,[tex]a_2=-4[/tex]
[tex]=\frac{-4}{\frac{-2}{3}}[/tex]
[tex]=\frac{4\times 3}{2}[/tex]
[tex]=\frac{12}{2}[/tex]
[tex]r=6[/tex]
[tex]r=\frac{a_3}{a_2}[/tex] here [tex]a_2=-4[/tex] and [tex]a_3=-24[/tex]
[tex]=\frac{-24}{-4}[/tex]
[tex]=6[/tex]
[tex]r=6[/tex]
Therefore the common ratio is 6
Therefore the given sequence is geometric sequence
The nth term of the geometric sequence is
[tex]a_n=a_1r^{n-1}[/tex]
The formula which describes the given geometric sequence is
[tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,...
[tex]=\frac{-2}{3}6^{x-1}[/tex] for x=1,2,3,...
Now verify that [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence or not
put x=1 and the value of [tex]a_1[/tex] in [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,...
we get [tex]f(1)=-\frac{2}{3}(6)^{1-1}[/tex]
[tex]=-\frac{2}{3}(6)^0[/tex]
[tex]=-\frac{2}{3}[/tex]
Therefore [tex]f(1)=-\frac{2}{3}[/tex]
put x=2 we get [tex]f(2)=-\frac{2}{3}(6)^{2-1}[/tex]
[tex]=-\frac{2}{3}(6)^1[/tex]
[tex]=-\frac{12}{3}[/tex]
Therefore [tex]f(2)=-4[/tex]
put x=3 we get [tex]f(3)=-\frac{2}{3}(6)^{3-1}[/tex]
[tex]=-\frac{2}{3}(6)^2[/tex]
[tex]=-\frac{2(36)}{3}[/tex]
Therefore [tex]f(3)=-24[/tex]
Therefore the sequence is f(1),f(2),f(3),...
Therefore the sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...
Hence the formula [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence is verified
Therefore the formula [tex]f(x)=-\frac{2}{3}(6)^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence
Answer:
a
Step-by-step explanation:
Significant Figures PracticeName________________________ Date_____________ Section________________
1. State the number of significant digits in each measurement. 1) 2804 m2) 2.84 km3) 5.029 m4) 0.003068 m5) 4.6 x 105 m 6) 4.06 x 10-5 m7) 750 m8) 75 m 9) 75,000 m 10) 75.00 m 11) 75,000.0 m 12) 10 cm 2. Round the following numbers as indicated:To four figures:3.68241721.860051375.6523112.51145.4673To one decimal place:1.35112.4735.6875247.5558.235To two decimal places:22.49479.25880.030623.412541.866323. Solve the following problems and report answers with appropriate number of significant digits.1) 6.201 cm + 7.4 cm + 0.68 cm +12.0 cm =
2) 1.6 km + 1.62 km +1200 km =
3) 8.264 g - 7.8 g =
4) 10.4168 m - 6.0 m =
5) 12.00 m+15.001 kg=
6) 1.31 cm x 2.3 cm =
7) 5.7621 m x 6.201 m = 8) 20.2 cm / 7.41 s =
Answer:1)2804m^2=4s.f
2)84Km^3=2s.f
3)5.029m=4s.f
4)0.00003068m=4s.f
5)4.6×10^5m=2s.f
6)4.06×10^-5m=3s.f
7)750m=3s.f
8)75m=2s.f
9)75,000.0m=5s.f
10)75.00m=2s.f
11)75,000.00m=5s.f
12)10cm=2s.t
B) to four significant figures
1)3.682
2)860100
3)375.7
4)51150
5)4673
C to 1 decimal places
1)1.4
2)4735.0
3)687524.0
4)7.6
5)235.0
Dto 2d.p
1)22.49
2)25880.00
3)30623.00
4)412541.00
5)866323.00
E)
1)6.201cm+7.4cm+0.68cm+12.0cm=26.281cm
2)1.6km+1.62km+1200km=1203.22km
3)8.264g-7.8g=0.464g
4)10.4168m-6m=4.4168m
5)12.00m+15.001kg=12.00m+15.001kg
6)1.31cm×2.3cm=3.013cm^2
7)5.7621m×6.201m=35.7308m^2
8)20.2cm/7.41s=2.726cm/s
Step-by-step explanation:
S.f means significant figures or Digits.
2)cm +kg is impossible because they are unlike termsi.e they do not have any thing in common, hence 12.00m+15.001kg cannot be added up.
This detailed answer involves the concept of significant figures, rounding off significant figures, and performing calculations while maintaining the appropriateness of significant figures in measurement.
Explanation:Number of significant digits
Significance figures involve the digits in a number that carry meaningful information about its precision.
2804 m - 4 significant digits2.84 km - 3 significant digits5.029 m - 4 significant digits0.003068 m - 4 significant digits4.6 x 10^5 m - 2 significant digits4.06 x 10^-5 m - 3 significant digits750 m - 2 significant digits75 m - 2 significant digits75,000 m - 2 significant digits (trailing zeros in a whole number do not count as significant figures)75.00 m - 4 significant digits (trailing zeros in a decimal number do count as significant figures)75,000.0 m - 6 significant digits.10 cm - 1 significant digit
Rounding off to Significant Figures
To round to a certain number of significant figures, start from the first non-zero number and count the number of digits required, rounding the last one if necessary. Here are your rounded numbers:
To four figures: 3.6825; 21.86; 375.7; 112.5; 45.67.To one decimal place: 1.4; 2.5; 5.7; 248; 8.2.To two decimal places: 22.49; 79.26; 80.03; 23.41; 41.87.
Performing Calculations
In adding or subtracting numbers, the result should retain the smallest number of decimal places in the input values. In multiplication or division, the result should retain the smallest number of significant figures in the input values. Here are your answers:
6.2 cm + 7.4 cm + 0.68 cm +12.0 cm = 26.3 cm.1.6 km + 1.62 km +1200 km = 1204 km.8.264 g - 7.8 g = 0.46 g.10.4168 m - 6.0 m = 4.4 m.Cannot add metres and kilograms - invalid calculation.1.31 cm x 2.3 cm = 3.0 cm^2.5.7621 m x 6.201 m = 35.728 m^2.20.2 cm / 7.41 s = 2.7 cm/s.Learn more about Significant Figures here:https://brainly.com/question/37022020
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A jar contains 11 green marbles, 7 red marbles, and 6 blue marbles. A marble is selected at random, not replaced, and then a second marble is selected. What is the probability of selecting a blue marble followed by a green marble?
Write In a fraction.
Answer:
11/92
Step-by-step explanation:
G = 11
R = 7
B = 6
P(b) = 6/24 = 1/4
P(g) = 11/23
P(blue first and then green(without replacement)) = 1/4 * 11/23
= 11/92
The probability of randomly selecting a blue marble followed by a green marble from a jar of 24 marbles (6 blue, 7 red, 11 green) is 11/92.
Explanation:The number of outcomes considered favorable or desired is compared to the total number of outcomes possible. In this situation, we're interested in choosing a blue marble first, then a green marble. The total number of marbles is 11 green + 7 red + 6 blue = 24 marbles.
Initially, the probability of selecting a blue marble is 6/24 = 1/4
because there are 6 blue marbles out of a total of 24.
After taking one marble out (assuming it's blue), you have 23 marbles left, with 11 of them being green. So, the probability of selecting a green marble next is 11/23.
Therefore, the probability of both of these events happening (selecting a blue marble followed by a green marble) is found by multiplying these two probabilities together, which gives (1/4) * (11/23) = 11/92.
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The sum of six fifths 6 5 and six timessix times a number is equal to four fifths 4 5 subtracted from seven timesseven times the number. Find the number.
Answer :
The required number is 2.
Step-by-step explanation:
Given : The sum of six fifths and six times a number is equal to four fifths subtracted from seven times the number.
To find : The number ?
Solution :
Let the number be 'x'.
The sum of six fifths and six times a number i.e. [tex]\frac{6}{5}+6x[/tex]
Four fifths subtracted from seven times the number i.e. [tex]7x-\frac{4}{5}[/tex]
According to question,
[tex]\frac{6}{5}+6x=7x-\frac{4}{5}[/tex]
[tex]7x-6x=\frac{6}{5}+\frac{4}{5}[/tex]
[tex]x=\frac{10}{5}[/tex]
[tex]x=2[/tex]
The required number is 2.
Divide the following polynomials. Then place the answer in the proper location on the grid. Write your answer in order of descending powers of x. Do not include parentheses in your answer.6x3 + 11x2 - 4x -4 / 3x - 2
Answer:
The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.
Step-by-step explanation:
We have attached the division for your reference.
Given:
Dividend = [tex]6x^3 + 11x^2 - 4x -4[/tex]
Divisor= [tex]3x - 2[/tex]
Explaining the division we get;
Step 1: First when we divide the Dividend [tex]6x^3 + 11x^2 - 4x -4[/tex] with divisor [tex]3x - 2[/tex] we will first multiply [tex]2x^2[/tex] with the divisor then we get the Quotient as [tex]2x^2[/tex] and Remainder as [tex]15x^2-4x-4[/tex]
Step 2: Now the Dividend is [tex]15x^2-4x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply [tex]5x[/tex] with the divisor then we get the Quotient as [tex]2x^2+5x[/tex] and Remainder as [tex]6x-4[/tex]
Step 3: Now the Dividend is [tex]6x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply 2 with the divisor then we get the Quotient as [tex]2x^2+5x+2[/tex] and Remainder as 0.
Hence The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.
The explicit formula for a sequence is
an=−1+3(n−1)
What is the 55th term of the sequence?
Step-by-step explanation:
[tex] \because \: a_n = - 1 + 3(n - 1) \\ \\ \therefore \: a_{55} = - 1 + 3(55 - 1) \\ \\ \therefore \: a_{55} = - 1 + 3 \times 54 \\ \\ \therefore \: a_{55} = - 1 + 162\\ \\ \huge \blue { \boxed{\therefore \: a_{55} = 161}}\\ \\ [/tex]
Hence, the 55th term of the sequence is 161.
How many days are there in one month? It is measured in the
A. thousands
B. tens
O ooo
c. ones
D. hundreds
Tens is the correct answer
If you were going to apply statistical methods to analyze teacher evaluations, which question form, A or B, would be better? Form A: In your own words, tell how this teacher compares with other teachers you have had. Form B: Use the following scale to rank your teacher as compared with other teachers you have had.a. Form B would be better because statistical methods can be applied to the ordinal data. b. Form B would be better because statistical methods can be applied to the nominal data. c. Form A would be better because statistical methods can be applied to the nominal data. e. Form A would be better because statistical methods can be applied to the ordinal data.
Answer:
a. Form B would be better because statistical methods can be applied to the ordinal data.
Step-by-step explanation:
Ordinal data can be ranked. This teacher evaluation can be ranked on a scale of 1-10 for example. Ordinal data can provide good information about the choice of the person who is responding. And these informations are quantitative in nature.
TRY IT! Simplity
x(x + 5)
2x2 - 50
Use differentiation to show that the given function is a solution of the equation for all values of the constants. (Enter your answers in terms of x.) equation: x'' + x = 2et, function x = C1 sin(t) + C2 cos(t) + et
Answer with Step-by-step explanation:
We are given that
DE
[tex]x''+x=2e^t[/tex]
Function:[tex]x=C_1sint+C_2cost+e^t[/tex]
We have to show that given function is a solution of the equation for all values of the constants.
If given function is solution of DE then it satisfied the given DE.
Differentiate function w.r.t.t
[tex]x'=C_1cost-C_2sint+e^t[/tex]
Again differentiate w.r.t. t
[tex]x''=-C_1sint-C_2cost+e^t[/tex]
Substitute the values in the given DE
[tex]-C_1sint-C_2cost+e^t+C_1sint+C_2cost+e^t=2e^t[/tex]
LHS=RHS
Given function satisfied the given DE.Therefore, it is solution of given DE for all values of the constants.
The perimeter of square JKLM is 48 units. Square J K L M is shown. The length of J K is x + 3. What is the value of x? 6 9 12 15
Answer:
x = 9
Step-by-step explanation:
if the perimeter os square JKLM is 48
each side has 48/4
so each side has 12
now if JK is x + 3 = 12
we only need to solve that
x + 3 = 12
x = 12 -3
x = 9
Answer:
B. 9
Step-by-step explanation:
Please help, I was absent for this day so I don't know how to do this.
Answer:
Step-by-step explanation:
An arc is a portion of the circle's circumference bounded by 2 radii
The formula for determining the length of an arc is expressed as
Length of arc = θ/360 × 2πr
Where
θ represents the central angle or angle which the 2 radii subtends at the center of the circle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Radius, r = 5 inches
θ = 170 degrees
Therefore,
Length of arc = 170/360 × 2 × π × 5
Length of arc = 4.7222π feet
rounding up to 2 decimal places, it becomes
4.72π feet
If six cookies cost the same as 2 brownies, and four brownies cost the same as 10 cupcakes, how many cupcakes can Bob buy for the price of eighteen cookies?
Bob can buy 15 cupcakes for the price of 18 cookies.
Step-by-step explanation:
Assume the cost of a cookie is $x, the cost of a brownie is $y and the cost of a cupcake is $z.It is given that 6 cookies and 2 brownies cost the same, so 6x = 2y, take this as equation 1.It is also given that 4 brownies cost the same as 10 cupcakes, so 4y = 10z, take this as equation 2.If we divide equation 2 by 2 we get, 2y = 5z so that the y value is the same as equation 1 and we can equate equation 1 and 3.We get 6x = 2y = 5z, 6x = 5z, dividing both sides by 5, we get 1.2x = z.We need to calculate how many cupcakes Bob can buy for the price of 18 cookies, So we must find the z value when the x = 18.If we multiply 1.2 with 15 we get 18 so we the last equation is multiplied with 12 so that 18x = 15z. 18 cookies and 15 cupcakes cost the same.PLZ HURRY IT'S URGENT!!
Which fraction represents the ratio 9 to 6 in simplest form?
1/6
6/9
3/2
9/2
Answer:
3/2
Step-by-step explanation:
Answer:
3/2
Step-by-step explanation:
9 to 6 means
[tex]\dfrac{9}{6}[/tex]
Now we will cancel that fraction - we will divide numerator and denominator both by 3:
9 divided by 3 equals 3
6 divided by 3 equals 2
Hence,
[tex]\dfrac{9}{6} = \dfrac{3\cdot 3}{2\cdot 3} = \dfrac{3}{2}[/tex]
These two ways of setting up a String yield identical results: a) String string = new String("123.45"); b) String string = "" + 123.45; Group of answer choices True False
Answer:
Step-by-step explanation:
Simplify.
4n + 12 + 7n
16n + 7
23n
11n + 12
4n + 19
In the context of data patterns in a time series, a(n) _____ is a one-time variation that is explainable.
Final answer:
In a time series, an explainable one-time variation is known as an outlier. Outliers can be important for understanding data, but they differ from inexplicable random components which include variations not explained by trend, cyclical, or seasonal patterns.
Explanation:
In the context of data patterns in a time series, a one-time variation that is explainable is usually referred to as an outlier. An outlier can be a potential key to understanding the data or it may be due to some abnormality or error. In a time series, data is analyzed over time to determine components such as the trend, cyclical, seasonal, and random components.
Trend component displays the long-term progression of the series, the cyclical component deals with fluctuations occurring at non-fixed intervals, the seasonal component reflects regular variations within a specific period, like quarters within a year, and the random component comprises those elements that cannot be attributed to the trend, cyclical, or seasonal patterns.
It's essential to distinguish outliers from the random components, which are, by definition, inexplicable variations. However, if an outlier can be explained by a particular event or change, it's not part of the random component but a distinct deviation from the expected pattern.
The ratio of the weight of an object on Mars to its weight on Earth is 9 to 25. If a person weighs 120 pounds on Earth, how much would the person weigh on Mars?
Answer:
Wm = 43.2 pounds
Step-by-step explanation:
If the ratio of the weight of an object on Mars to its weight on Earth is 9 to 25, this means that what on Mars weighs 9 units on earth weighs 25 units, therefore:
Data
ratio = 9/25
Weight on Mars (Wm) = ?
Weight on Earth (We) = 120 pound
Wm = (9/25)*120 pound = 43.2 pounds
Trista had 95 correct out of 100 problems on her math test. The ratio of correct answers to total problems is . Written in fraction form, this is . Written as a percent, Trista got of the problems correct.
Answer:
Fractional form = [tex]\frac{95}{100}=\frac{19}{20}[/tex]
Percent form = 95%
Trisha got 95% of her problems correct.
Step-by-step explanation:
Given:
Total number of questions (N) = 100
Number of correct questions (C) = 95
Therefore, the ratio of the correct answers to the total number of problems is given by dividing the the number of correct questions by the total number of questions. This is given as:
Ratio expressed as a fraction = [tex]\frac{C}{N}=\frac{95}{100}=\frac{95\div 5}{100\div 5}=\frac{19}{20}(Simplest\ form)[/tex]
Now in order to express this ratio in percentage form, we need to multiply the given ratio by 100. This gives,
Ratio expressed as a percent = [tex]\frac{C}{N}\times 100=\frac{95}{100}\times 100=95\%[/tex]
Therefore, Trisha got 95% of her problems correct.
Answer:
1: the first one
2:the third one
3:the third one
Step-by-step explanation:
Help plz if you know this then plz answer back! How do you solve (x to the power of -1) (x to the power of -5) The lesson is multiplying and dividing expressions with exponents.
Answer:
(x⁻¹)(x⁻⁵) = x⁻⁶
Step-by-step explanation:
When multiplying number with the same base, you add up their exponent.
(x⁻¹)(x⁻⁵) =
= x⁽⁻¹⁾ ⁺ ⁽⁻⁵⁾
= x⁻⁶
you can also write x⁻⁶ as 1/x⁶. The negative sign in the exponent just flip the numerator and denominator with each others.
Answer:
The answer to your question is x⁻⁶ or 1/x⁶
Step-by-step explanation:
Multiplying exponents
-To multiply exponents they must have the same base and the result will be the base and the exponents will add.
Ex
(a³)(a²)
base = a
exponents = 3 and 2
result a³ ⁺ ² = a⁵
In your question
(x⁻¹)(x⁻⁵) = x⁻¹⁻⁵ = x⁻⁶ = 1/x⁻⁶
FIND THE INVERSE OF -5 + 7i
Answer:
Additive inverses for complex numbers are just like they are for real numbers: they mean the number you'd add to get back to 0. Just like real numbers, this means that you change the signs. Thus, the additive inverse of -4+7i is 4-7i
hope it helps
Step-by-step explanation:
You are designing a staircase to reach a second floor that is 113" above the ground floor of a building. The owner of the building wants you to make a staircase as close as possible to a 7.25" rise to meet their specifications
Answer:
Step-by-step explanation:
total height, H = 113 inches
height of each stair case, h = 7.25 inches
Number of stair case, n = total height / height of each stair case
n = 113 / 7.25 = 15.6
The longest human power sporting event is the tour de France cycling race in a particular year the average speed for the winner of the this race was 23.66 mph in that same year of the race was 2292 miles long how long did it take the winner to complete the race
Answer:
The winner completed the race in 96 hours and 52 minutes.
Step-by-step explanation:
Given:
Distance of the cycling race = 2292 miles
Average speed of the winner = [tex]23.66\ mph[/tex]
We need to find time required by winner to complete the race.
Solution:
Now we know that;
Time required can be calculated by dividing Total Distance from the Average speed.
framing in equation form we get;
time required by winner to complete the race = [tex]\frac{2292}{23.66} = 96.87\ hrs[/tex]
Now converting [tex]0.87\ hrs[/tex] into minutes we get;
[tex]0.87\times 60= 52.2\approx 52\ mins[/tex]
Hence the winner completed the race in 96 hours and 52 minutes.
In AABC, 2B= 2C, and m_A= 349. Find mzo
A. 56°
B. 730
c. 112°
1460
Answer:
i think it' =-8abc(a+b-c)
Step-by-step explanation:
The variables x and y are proportional.Use the vaules to find the constant aof proportonality.Then write the equation that relates x and y. When y=72, and x=3
Answer:
Constant of proportionality = 24
Equation: [tex]y=24x[/tex]
Step-by-step explanation:
Given:
'x' and 'y' are proportional to each other.
At [tex]x=3,y=72[/tex]
Now, for a proportional relationship, the constant of proportionality is given as the ratio of the two values of the two variables that are in proportion.
Here, 'x' and 'y' are in proportion. So, the constant of proportionality is given as:
[tex]k=\frac{y}{x}\\\\k=\frac{72}{3}=24[/tex]
Therefore, the constant of proportionality is 24.
Now, a proportional relationship in 'x' and 'y' is given as:
[tex]y=kx[/tex]
Now, plug in the given value of 'k' and complete the equation. This gives,
[tex]y=24x[/tex]
Therefore, the equation that relates 'x' and 'y' is [tex]y=24x[/tex]
Right △EFG has its right angle at G, EF=8 , and FG=6 .
What is the value of the trigonometric ratio of an angle of the triangle?
Drag a value to each box to match the trigonometric ratio with its value.
Answer:
[tex]sec\ E = \frac{4\sqrt{7} }{7}[/tex]
[tex]Cos\ F = \frac{3}{4}[/tex]
[tex]Tan\ F =\frac{\sqrt{7}}{3}[/tex]
Step-by-step explanation:
Given
EF = 8
FG = 6
We need to find the trigonometric ratios.
Solution:
First we will find the length of the third side.
Now we know that;
△EFG is a right angled triangle with right angle at G.
Now applying Pythagoras theorem which states.
"The sum of square of the two legs of the triangle is equal to square of the hypotenuse."
so we can say that;
[tex]FG^2=EF^2+EG^2\\\\EG^2=FG^2-EF^2[/tex]
Substituting the given values we get;
[tex]EG^2=8^2-6^2=64-36=28[/tex]
Taking square roots on both side we get;
[tex]\sqrt{EG^2} =\sqrt{28}=\sqrt{4\times7}\\ \\EG = 2\sqrt{7}[/tex]
Now we will find the trigonometric values.
[tex]secE=\frac{Hypotenuse}{Adjacent\ side}[/tex]
Here Hypotenuse = EF = 8
Adjacent side of E = EG = [tex]2\sqrt{7}[/tex]
[tex]secE=\frac{8}{2\sqrt{7}} =\frac{4}{\sqrt{7}}[/tex]
Now rationalizing the denominator by multiplying numerator and denominator by [tex]\sqrt{7}[/tex] we get;
[tex]secE=\frac{4\times \sqrt{7} }{\sqrt{7}\times \sqrt{7} }\\\\secE = \frac{4\sqrt{7} }{7}[/tex]
Now,
[tex]Cos F = \frac{Adjacent \ side}{Hypotenuse}[/tex]
Adjacent side to F =GF = 6
Hypotenuse = EF = 8
[tex]Cos\ F = \frac{6}{8}\\\\Cos\ F = \frac{3}{4}[/tex]
Now,
[tex]Tan F = \frac{opposite \ side}{adjacent\ side}[/tex]
Here Opposite side of F = EG = [tex]2\sqrt{7}[/tex]
Adjacent side of F = GF = 6
[tex]Tan\ F= \frac{2\sqrt{7}}{6}\\\\Tan\ F =\frac{\sqrt{7}}{3}[/tex]
Hence Below are required details.
[tex]sec\ E = \frac{4\sqrt{7} }{7}[/tex]
[tex]Cos\ F = \frac{3}{4}[/tex]
[tex]Tan\ F =\frac{\sqrt{7}}{3}[/tex]
The value of the trigonometric ratio of an angle of the triangle is;
[tex]\rm SecE=\dfrac{8}{2\sqrt{7}}=\dfrac{4}{\sqrt{7} }\\\\CosF = \dfrac{6}{8}=\dfrac{3}{4}\\\\Tan F =\dfrac{2\sqrt{7}}{3}=\dfrac{\sqrt{7} }{3}\\[/tex]
Given
Right △EFG has its right angle at G, EF=8, and FG=6.
Pythagoras theoremThe Pythagoras theorem states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of the other two sides of the right-angled triangle.
In right-angle △EFG, in which E is a right angle.
[tex]\rm EF^2=FG^2-EG^2\\\\8^2=6^2-EG^2\\\\EG^2=8^2-6^2\\ \\EG^2=64-36\\\\EG^2=28\\\\EG = 2\sqrt{7}[/tex]
The value of the trigonometric ratio of an angle of the triangle is;
[tex]\rm SecE=\dfrac{8}{2\sqrt{7}}=\dfrac{4}{\sqrt{7} }\\\\CosF = \dfrac{6}{8}=\dfrac{3}{4}\\\\Tan F =\dfrac{2\sqrt{7}}{3}=\dfrac{\sqrt{7} }{3}\\[/tex]
To know more about the Pythagoras theorem click the link given below.
https://brainly.com/question/15359190
Maytag wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 6060 customers and asks them about their level of satisfaction with the company. What type of sampling is used?
a. Simple random
b. Cluster
c. Systematic
d. Stratified
e. Convenience
Answer:
Correct answer is (a). Simple random sampling
Step-by-step explanation:
Simple random sampling (SRS) is a statistical techniques used in choosing subset of members of the population randomly without given special priority to anyone to be chosen. It gives every members of the population equal chance.
By randomly selecting 6060 customers from the customer's database, Maytag has employed Simple Random Sampling method of survey.
Which of the following is the image of the point for the given rotation, r (120°) (F)?
Answer:
B
Step-by-step explanation:
360/6
6 is number of sides
You get 60
Rotate twice to reach 120
Moving F Counter clockwise twice is where B was
The image of point F after the rotation of 120°, r(120°), will be point B.
Which point will represent the given rotation of F?
So, we need to rotate point F a total angle of 120°.
As you can see, in the image we have 6 sections, and equally distributed in these 6 sections we will have an angle of 360° (a complete rotation). So each section has an angle of:
360°/6 = 60°.
Then a rotation of 120° (two times 60°) will rotate the point F two sections counterclockwise. Then the image of the point after the rotation will be point B.
If you want to learn more about rotations, you can read:
https://brainly.com/question/4289712
Kenneth measured a hotel and made a scale drawing the scale he used was 1 inch= 4 feet the actual length of a room in the hotel is 20 feel how long is the room in the drawing
Answer:
The length of the room in the drawing is 5 inches.
Step-by-step explanation:
Given:
Kenneth measured a hotel and made a scale drawing the scale he used was 1 inch= 4 feet.
The actual length of a room in the hotel is 20 feet.
Now, to find the length of the room in the drawing.
Let the length of the room in the drawing be [tex]x.[/tex]
The actual length of the room = 20 feet.
The scale used in drawing is 1 inch = 4 feet.
As, 1 inch is equivalent to 4 feet.
Thus, [tex]x[/tex] is equivalent to 20 feet.
Now, to get the length of the room in the drawing we use cross multiplication method:
[tex]\frac{1}{4} =\frac{x}{20}[/tex]
By cross multiplying we get:
[tex]20=4x[/tex]
Dividing both sides by 4 we get:
[tex]5=x[/tex]
[tex]x=5\ inches.[/tex]
Therefore, the length of the room in the drawing is 5 inches.